1. Because Aqua Coat is water-based, so is less likely to remove some of it when applied.
2. Won't raise the grain like water-based stains will, so no extra sanding is required.
3. Spirit-based stains penetrate that bit further into the wood. Only a bit further, but it all helps get a consistent colour.
4. I feel that they are easier to apply without leaving tide-marks. It's a lot easier to blend any small tide-marks back in than with water-based.

I wouldn't use it if I had any curved binding. I don't know if it's just the Chinese stuff the kits use, but anywhere on the binding with any sort of curve, you get tiny stress cracks forming in the plastic. The sharper the curve, the more cracks you get. Straight binding seems to be OK, e.g. binding on a neck. You can't see the cracks with your eyes. But spirit-based stain is thinner and has a lower surface tension than water-based stain, so whilst water-based stain may find and sit at the top of the very largest cracks, this can normally be scraped off. Spirit-based stain will find every single crack and work its way down to the bottom, of the crack which can be 1-2mm deep in places and can't be removed by scraping. Even masking the binding doesn't guarantee that it won't seep in.